Processes and systems for forecasting metric data and anomaly detection in a distributed computing system

ABSTRACT

Computational processes and systems are directed to forecasting time series data and detection of anomalous behaving resources of a distributed computing system data. Processes and systems comprise off-line and on-line modes that accelerate the forecasting process and identification of anomalous behaving resources. In the off-line mode, recurrent neural network (“RNN”) is continuously trained using time series data associated with various resources of the distributed computing system. In the on-line mode, the latest RNN is used to forecast time series data for resources in a forecast time window and confidence bounds are computed over the forecast time window. The forecast time series data characterizes expected resource usage over the forecast time window so that usage of the resource may be adjusted. The confidence bounds may be used to detect anomalous behaving resources. Remedial measures may then be executed to correct problems indicated by the anomalous behavior.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of Provisional Application No.62/722,640 filed Aug. 24, 2018.

TECHNICAL FIELD

This disclosure is directed to processes and systems that forecast timeseries metric data and detect anomalous behaving resources of adistributed computing system.

BACKGROUND

Electronic computing has evolved from primitive, vacuum-tube-basedcomputer systems, initially developed during the 1940s, to modernelectronic computing systems in which large numbers of multi-processorcomputer systems, such as server computers, work stations, and otherindividual computing systems are networked together with large-capacitydata-storage devices and other electronic devices to producegeographically distributed computing systems with numerous componentsthat provide enormous computational bandwidths and data-storagecapacities. These large, distributed computing systems are made possibleby advances in computer networking, distributed operating systems andapplications, data-storage appliances, computer hardware, and softwaretechnologies.

Because distributed computing systems have an enormous number ofcomputational resources, various management systems have been developedto collect performance information about these resources. For example, atypical management system may collect hundreds of thousands of streamsof metric data to monitor various computational resources of a datacenter infrastructure. Each data point of a stream of metric data mayrepresent an amount of the resource in use at a point in time. However,the enormous number of metric data streams received by a managementsystem makes it impossible for information technology (“IT”)administrators to manually monitor the metrics, detect performanceissues, and respond in real time. Failure to respond in real time toperformance problems can interrupt computer services and have enormouscost implications for data center tenants, such as when a tenant'sserver applications stop running or fail to timely respond to clientrequests.

SUMMARY

Computational processes and systems described herein are directed toforecasting time series data and anomaly detection with forecast timeseries data generated in a distributed computing system using arecurrent neural network (“RNN”). Processes and systems compriseoff-line and on-line modes that accelerate the forecasting process andidentification of anomalous behaving resources. The off-line modecontinuously trains an RNN using time series data recorded in a timeseries database for various resources of the distributed computingsystem. The on-line mode uses the latest RNN trained in the off-linemode to forecast time series data over a forecast time window for aresource of a tenant environment of the distributed computing system.The forecast time series data characterizes expected resource usage overthe forecast time window. Processes and systems compute correspondingconfidence bounds based on the time series database. The confidencebounds may be used to detect anomalous behavior of the resource.Remedial measures may then be executed to correct problems indicated bythe anomalous behavior.

DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an architectural diagram for various types of computers.

FIG. 2 shows an Internet-connected distributed computer system.

FIG. 3 shows cloud computing.

FIG. 4 shows generalized hardware and software components of ageneral-purpose computer system.

FIGS. 5A-5B show two types of virtual machine (“VM”) and VM executionenvironments.

FIG. 6 shows an example of an open virtualization format package.

FIG. 7 shows virtual data centers provided as an abstraction ofunderlying physical-data-center hardware components.

FIG. 8 shows virtual-machine components of a virtual-data-centermanagement server and physical servers of a physical data center.

FIG. 9 shows a cloud-director level of abstraction.

FIG. 10 shows virtual-cloud-connector nodes.

FIG. 11 shows an example server computer used to host three containers.

FIG. 12 shows an approach to implementing containers on a VM.

FIG. 13A show an example of a virtualization layer located above aphysical data center.

FIGS. 13B-13C shows streams of metric time series data transmitted to amonitor tool.

FIG. 14 shows a plot of an example sequence of time series dataassociated with a resource of a distributed computing system.

FIG. 15 shows a high-level view of a process for forecasting time seriesdata and generating confidence bounds.

FIG. 16 shows a workflow of the off-line mode of FIG. 15.

FIGS. 17A-17B show training of a recurrent neural network (“RNN”) andcomputation of forecast errors, respectively.

FIG. 18 shows a workflow of the on-line mode of FIG. 15.

FIG. 19 shows a process for computing forecast time series data withconfidence bounds for time series data from a tenant environment.

FIGS. 20A-20B illustrate computing forecast time series data in aforecast time window and applying confidence bounds to the forecast timeseries data.

FIGS. 21A-21J show plots of results obtained from training and using anRNN to forecast time series data and generate confidence bounds for CPUand memory time series data.

FIG. 22 shows a control-flow diagram of a method to compute forecasttime series data and identify anomalous behaving resources of adistributed computing system.

FIG. 23 shows a control-flow diagram of routine “train RNN based onhistorical time series database and compute confidence bounds of timeseries database” called in FIG. 22.

FIG. 24 shows a control-flow diagram of the routine “train RNN usingtime series database” called in FIG. 23.

FIG. 25 shows a control-flow diagram of the routine “compute confidencebounds for the time series database” called in FIG. 23.

FIG. 26 shows a control-flow diagram of the routine “compute forecasttime series data in forecast time window” called in FIG. 22.

FIG. 27 shows a control-flow diagram of the routine “identify abnormalbehavior of resource based on confidence bounds” called in FIG. 22.

FIG. 28 shows a control-flow diagram of the routine “report abnormalbehavior/execute remedial measures” called in FIG. 22.

DETAILED DESCRIPTION

This disclosure is directed to computational processes and systems thatforecast time series data and detect anomalous behaving resources of adistributed computing system. In a first subsection, computer hardware,complex computational systems, and virtualization are described.Processes and systems for forecasting time series data and detection ofanomalous behaving resources of a distributed computing system aredescribed below in a second subsection.

Computer Hardware, Complex Computational Systems, and Virtualization

The term “abstraction” is not, in any way, intended to mean or suggestan abstract idea or concept. Computational abstractions are tangible,physical interfaces that are implemented using physical computerhardware, data-storage devices, and communications systems. Instead, theterm “abstraction” refers, in the current discussion, to a logical levelof functionality encapsulated within one or more concrete, tangible,physically-implemented computer systems with defined interfaces throughwhich electronically-encoded data is exchanged, process executionlaunched, and electronic services are provided. Interfaces may includegraphical and textual data displayed on physical display devices as wellas computer programs and routines that control physical computerprocessors to carry out various tasks and operations and that areinvoked through electronically implemented application programminginterfaces (“APIs”) and other electronically implemented interfaces.Software is essentially a sequence of encoded symbols, such as aprintout of a computer program or digitally encoded computerinstructions sequentially stored in a file on an optical disk or withinan electromechanical mass-storage device. Software alone can do nothing.It is only when encoded computer instructions are loaded into anelectronic memory within a computer system and executed on a physicalprocessor that “software implemented” functionality is provided. Thedigitally encoded computer instructions are a physical control componentof processor-controlled machines and devices. Multi-cloud aggregations,cloud-computing services, virtual-machine containers and virtualmachines, containers, communications interfaces, and many of the othertopics discussed below are tangible, physical components of physical,electro-optical-mechanical computer systems.

FIG. 1 shows a general architectural diagram for various types ofcomputers. Computers that receive, process, and store event messages maybe described by the general architectural diagram shown in FIG. 1, forexample. The computer system contains one or multiple central processingunits (“CPUs”) 102-105, one or more electronic memories 108interconnected with the CPUs by a CPU/memory-subsystem bus 110 ormultiple busses, a first bridge 112 that interconnects theCPU/memory-subsystem bus 110 with additional busses 114 and 116, orother types of high-speed interconnection media, including multiple,high-speed serial interconnects. These busses or serialinterconnections, in turn, connect the CPUs and memory with specializedprocessors, such as a graphics processor 118, and with one or moreadditional bridges 120, which are interconnected with high-speed seriallinks or with multiple controllers 122-127, such as controller 127, thatprovide access to various different types of mass-storage devices 128,electronic displays, input devices, and other such components,subcomponents, and computational devices. It should be noted thatcomputer-readable data-storage devices include optical andelectromagnetic disks, electronic memories, and other physicaldata-storage devices. Those familiar with modern science and technologyappreciate that electromagnetic radiation and propagating signals do notstore data for subsequent retrieval, and can transiently “store” only abyte or less of information per mile, far less information than neededto encode even the simplest of routines.

Of course, there are many different types of computer-systemarchitectures that differ from one another in the number of differentmemories, including different types of hierarchical cache memories, thenumber of processors and the connectivity of the processors with othersystem components, the number of internal communications busses andserial links, and in many other ways. However, computer systemsgenerally execute stored programs by fetching instructions from memoryand executing the instructions in one or more processors. Computersystems include general-purpose computer systems, such as personalcomputers (“PCs”), various types of server computers and workstations,and higher-end mainframe computers, but may also include a plethora ofvarious types of special-purpose computing devices, includingdata-storage systems, communications routers, network nodes, tabletcomputers, and mobile telephones.

FIG. 2 shows an Internet-connected distributed computer system. Ascommunications and networking technologies have evolved in capabilityand accessibility, and as the computational bandwidths, data-storagecapacities, and other capabilities and capacities of various types ofcomputer systems have steadily and rapidly increased, much of moderncomputing now generally involves large distributed systems and computersinterconnected by local networks, wide-area networks, wirelesscommunications, and the Internet. FIG. 2 shows a typical distributedsystem in which many PCs 202-205, a high-end distributed mainframesystem 210 with a large data-storage system 212, and a large computercenter 214 with large numbers of rack-mounted server computers or bladeservers all interconnected through various communications and networkingsystems that together comprise the Internet 216. Such distributedcomputing systems provide diverse arrays of functionalities. Forexample, a PC user may access hundreds of millions of different websites provided by hundreds of thousands of different web serversthroughout the world and may access high-computational-bandwidthcomputing services from remote computer facilities for running complexcomputational tasks.

Until recently, computational services were generally provided bycomputer systems and data centers purchased, configured, managed, andmaintained by service-provider organizations. For example, an e-commerceretailer generally purchased, configured, managed, and maintained a datacenter including numerous web server computers, back-end computersystems, and data-storage systems for serving web pages to remotecustomers, receiving orders through the web-page interface, processingthe orders, tracking completed orders, and other myriad different tasksassociated with an e-commerce enterprise.

FIG. 3 shows cloud computing. In the recently developed cloud-computingparadigm, computing cycles and data-storage facilities are provided toorganizations and individuals by cloud-computing providers. In addition,larger organizations may elect to establish private cloud-computingfacilities in addition to, or instead of, subscribing to computingservices provided by public cloud-computing service providers. In FIG.3, a system administrator for an organization, using a PC 302, accessesthe organization's private cloud 304 through a local network 306 andprivate-cloud interface 308 and accesses, through the Internet 310, apublic cloud 312 through a public-cloud services interface 314. Theadministrator can, in either the case of the private cloud 304 or publiccloud 312, configure virtual computer systems and even entire virtualdata centers and launch execution of application programs on the virtualcomputer systems and virtual data centers in order to carry out any ofmany different types of computational tasks. As one example, a smallorganization may configure and run a virtual data center within a publiccloud that executes web servers to provide an e-commerce interfacethrough the public cloud to remote customers of the organization, suchas a user viewing the organization's e-commerce web pages on a remoteuser system 316.

Cloud-computing facilities are intended to provide computationalbandwidth and data-storage services much as utility companies provideelectrical power and water to consumers. Cloud computing providesenormous advantages to small organizations without the devices topurchase, manage, and maintain in-house data centers. Such organizationscan dynamically add and delete virtual computer systems from theirvirtual data centers within public clouds in order to trackcomputational-bandwidth and data-storage needs, rather than purchasingsufficient computer systems within a physical data center to handle peakcomputational-bandwidth and data-storage demands. Moreover, smallorganizations can completely avoid the overhead of maintaining andmanaging physical computer systems, including hiring and periodicallyretraining information-technology specialists and continuously payingfor operating-system and database-management-system upgrades.Furthermore, cloud-computing interfaces allow for easy andstraightforward configuration of virtual computing facilities,flexibility in the types of applications and operating systems that canbe configured, and other functionalities that are useful even for ownersand administrators of private cloud-computing facilities used by asingle organization.

FIG. 4 shows generalized hardware and software components of ageneral-purpose computer system, such as a general-purpose computersystem having an architecture similar to that shown in FIG. 1. Thecomputer system 400 is often considered to include three fundamentallayers: (1) a hardware layer or level 402; (2) an operating-system layeror level 404; and (3) an application-program layer or level 406. Thehardware layer 402 includes one or more processors 408, system memory410, different types of input-output (“I/O”) devices 410 and 412, andmass-storage devices 414. Of course, the hardware level also includesmany other components, including power supplies, internal communicationslinks and busses, specialized integrated circuits, many different typesof processor-controlled or microprocessor-controlled peripheral devicesand controllers, and many other components. The operating system 404interfaces to the hardware level 402 through a low-level operatingsystem and hardware interface 416 generally comprising a set ofnon-privileged computer instructions 418, a set of privileged computerinstructions 420, a set of non-privileged registers and memory addresses422, and a set of privileged registers and memory addresses 424. Ingeneral, the operating system exposes non-privileged instructions,non-privileged registers, and non-privileged memory addresses 426 and asystem-call interface 428 as an operating-system interface 430 toapplication programs 432-436 that execute within an executionenvironment provided to the application programs by the operatingsystem. The operating system, alone, accesses the privilegedinstructions, privileged registers, and privileged memory addresses. Byreserving access to privileged instructions, privileged registers, andprivileged memory addresses, the operating system can ensure thatapplication programs and other higher-level computational entitiescannot interfere with one another's execution and cannot change theoverall state of the computer system in ways that could deleteriouslyimpact system operation. The operating system includes many internalcomponents and modules, including a scheduler 442, memory management444, a file system 446, device drivers 448, and many other componentsand modules. To a certain degree, modern operating systems providenumerous levels of abstraction above the hardware level, includingvirtual memory, which provides to each application program and othercomputational entities a separate, large, linear memory-address spacethat is mapped by the operating system to various electronic memoriesand mass-storage devices. The scheduler orchestrates interleavedexecution of different application programs and higher-levelcomputational entities, providing to each application program a virtual,stand-alone system devoted entirely to the application program. From theapplication program's standpoint, the application program executescontinuously without concern for the need to share processor devices andother system devices with other application programs and higher-levelcomputational entities. The device drivers abstract details ofhardware-component operation, allowing application programs to employthe system-call interface for transmitting and receiving data to andfrom communications networks, mass-storage devices, and other I/Odevices and subsystems. The file system 446 facilitates abstraction ofmass-storage-device and memory devices as a high-level, easy-to-access,file-system interface. Thus, the development and evolution of theoperating system has resulted in the generation of a type ofmulti-faceted virtual execution environment for application programs andother higher-level computational entities.

While the execution environments provided by operating systems haveproved to be an enormously successful level of abstraction withincomputer systems, the operating-system-provided level of abstraction isnonetheless associated with difficulties and challenges for developersand users of application programs and other higher-level computationalentities. One difficulty arises from the fact that there are manydifferent operating systems that run within different types of computerhardware. In many cases, popular application programs and computationalsystems are developed to run on only a subset of the available operatingsystems and can therefore be executed within only a subset of thedifferent types of computer systems on which the operating systems aredesigned to run. Often, even when an application program or othercomputational system is ported to additional operating systems, theapplication program or other computational system can nonetheless runmore efficiently on the operating systems for which the applicationprogram or other computational system was originally targeted. Anotherdifficulty arises from the increasingly distributed nature of computersystems. Although distributed operating systems are the subject ofconsiderable research and development efforts, many of the popularoperating systems are designed primarily for execution on a singlecomputer system. In many cases, it is difficult to move applicationprograms, in real time, between the different computer systems of adistributed computer system for high-availability, fault-tolerance, andload-balancing purposes. The problems are even greater in heterogeneousdistributed computer systems which include different types of hardwareand devices running different types of operating systems. Operatingsystems continue to evolve, as a result of which certain olderapplication programs and other computational entities may beincompatible with more recent versions of operating systems for whichthey are targeted, creating compatibility issues that are particularlydifficult to manage in large distributed systems.

For the above reasons, a higher level of abstraction, referred to as the“virtual machine,” (“VM”) has been developed and evolved to furtherabstract computer hardware in order to address many difficulties andchallenges associated with traditional computing systems, including thecompatibility issues discussed above. FIGS. 5A-B show two types of VMand virtual-machine execution environments. FIGS. 5A-B use the sameillustration conventions as used in FIG. 4. FIG. 5A shows a first typeof virtualization. The computer system 500 in FIG. 5A includes the samehardware layer 502 as the hardware layer 402 shown in FIG. 4. However,rather than providing an operating system layer directly above thehardware layer, as in FIG. 4, the virtualized computing environmentshown in FIG. 5A features a virtualization layer 504 that interfacesthrough a virtualization-layer/hardware-layer interface 506, equivalentto interface 416 in FIG. 4, to the hardware. The virtualization layer504 provides a hardware-like interface to VMs, such as VM 510, in avirtual-machine layer 511 executing above the virtualization layer 504.Each VM includes one or more application programs or other higher-levelcomputational entities packaged together with an operating system,referred to as a “guest operating system,” such as application 514 andguest operating system 516 packaged together within VM 510. Each VM isthus equivalent to the operating-system layer 404 andapplication-program layer 406 in the general-purpose computer systemshown in FIG. 4. Each guest operating system within a VM interfaces tothe virtualization layer interface 504 rather than to the actualhardware interface 506. The virtualization layer 504 partitions hardwaredevices into abstract virtual-hardware layers to which each guestoperating system within a VM interfaces. The guest operating systemswithin the VMs, in general, are unaware of the virtualization layer andoperate as if they were directly accessing a true hardware interface.The virtualization layer 504 ensures that each of the VMs currentlyexecuting within the virtual environment receive a fair allocation ofunderlying hardware devices and that all VMs receive sufficient devicesto progress in execution. The virtualization layer 504 may differ fordifferent guest operating systems. For example, the virtualization layeris generally able to provide virtual hardware interfaces for a varietyof different types of computer hardware. This allows, as one example, aVM that includes a guest operating system designed for a particularcomputer architecture to run on hardware of a different architecture.The number of VMs need not be equal to the number of physical processorsor even a multiple of the number of processors.

The virtualization layer 504 includes a virtual-machine-monitor module518 (“VMM”) that virtualizes physical processors in the hardware layerto create virtual processors on which each of the VMs executes. Forexecution efficiency, the virtualization layer attempts to allow VMs todirectly execute non-privileged instructions and to directly accessnon-privileged registers and memory. However, when the guest operatingsystem within a VM accesses virtual privileged instructions, virtualprivileged registers, and virtual privileged memory through thevirtualization layer 504, the accesses result in execution ofvirtualization-layer code to simulate or emulate the privileged devices.The virtualization layer additionally includes a kernel module 520 thatmanages memory, communications, and data-storage machine devices onbehalf of executing VMs (“VM kernel”). The VM kernel, for example,maintains shadow page tables on each VM so that hardware-levelvirtual-memory facilities can be used to process memory accesses. The VMkernel additionally includes routines that implement virtualcommunications and data-storage devices as well as device drivers thatdirectly control the operation of underlying hardware communications anddata-storage devices. Similarly, the VM kernel virtualizes various othertypes of I/O devices, including keyboards, optical-disk drives, andother such devices. The virtualization layer 504 essentially schedulesexecution of VMs much like an operating system schedules execution ofapplication programs, so that the VMs each execute within a complete andfully functional virtual hardware layer.

FIG. 5B shows a second type of virtualization. In FIG. 5B, the computersystem 540 includes the same hardware layer 542 and operating systemlayer 544 as the hardware layer 402 and the operating system layer 404shown in FIG. 4. Several application programs 546 and 548 are shownrunning in the execution environment provided by the operating system544. In addition, a virtualization layer 550 is also provided, incomputer 540, but, unlike the virtualization layer 504 discussed withreference to FIG. 5A, virtualization layer 550 is layered above theoperating system 544, referred to as the “host OS,” and uses theoperating system interface to access operating-system-providedfunctionality as well as the hardware. The virtualization layer 550comprises primarily a VMM and a hardware-like interface 552, similar tohardware-like interface 508 in FIG. 5A. The hardware-layer interface552, equivalent to interface 416 in FIG. 4, provides an executionenvironment VMs 556-558, each including one or more application programsor other higher-level computational entities packaged together with aguest operating system.

In FIGS. 5A-5B, the layers are somewhat simplified for clarity ofillustration. For example, portions of the virtualization layer 550 mayreside within the host-operating-system kernel, such as a specializeddriver incorporated into the host operating system to facilitatehardware access by the virtualization layer.

It should be noted that virtual hardware layers, virtualization layers,and guest operating systems are all physical entities that areimplemented by computer instructions stored in physical data-storagedevices, including electronic memories, mass-storage devices, opticaldisks, magnetic disks, and other such devices. The term “virtual” doesnot, in any way, imply that virtual hardware layers, virtualizationlayers, and guest operating systems are abstract or intangible. Virtualhardware layers, virtualization layers, and guest operating systemsexecute on physical processors of physical computer systems and controloperation of the physical computer systems, including operations thatalter the physical states of physical devices, including electronicmemories and mass-storage devices. They are as physical and tangible asany other component of a computer since, such as power supplies,controllers, processors, busses, and data-storage devices.

A VM or virtual application, described below, is encapsulated within adata package for transmission, distribution, and loading into avirtual-execution environment. One public standard for virtual-machineencapsulation is referred to as the “open virtualization format”(“OVF”). The OVF standard specifies a format for digitally encoding a VMwithin one or more data files. FIG. 6 shows an OVF package. An OVFpackage 602 includes an OVF descriptor 604, an OVF manifest 606, an OVFcertificate 608, one or more disk-image files 610-611, and one or moredevice files 612-614. The OVF package can be encoded and stored as asingle file or as a set of files. The OVF descriptor 604 is an XMLdocument 620 that includes a hierarchical set of elements, eachdemarcated by a beginning tag and an ending tag. The outermost, orhighest-level, element is the envelope element, demarcated by tags 622and 623. The next-level element includes a reference element 626 thatincludes references to all files that are part of the OVF package, adisk section 628 that contains meta information about all of the virtualdisks included in the OVF package, a network section 630 that includesmeta information about all of the logical networks included in the OVFpackage, and a collection of virtual-machine configurations 632 whichfurther includes hardware descriptions of each VM 634. There are manyadditional hierarchical levels and elements within a typical OVFdescriptor. The OVF descriptor is thus a self-describing, XML file thatdescribes the contents of an OVF package. The OVF manifest 606 is a listof cryptographic-hash-function-generated digests 636 of the entire OVFpackage and of the various components of the OVF package. The OVFcertificate 608 is an authentication certificate 640 that includes adigest of the manifest and that is cryptographically signed. Disk imagefiles, such as disk image file 610, are digital encodings of thecontents of virtual disks and device files 612 are digitally encodedcontent, such as operating-system images. A VM or a collection of VMsencapsulated together within a virtual application can thus be digitallyencoded as one or more files within an OVF package that can betransmitted, distributed, and loaded using well-known tools fortransmitting, distributing, and loading files. A virtual appliance is asoftware service that is delivered as a complete software stackinstalled within one or more VMs that is encoded within an OVF package.

The advent of VMs and virtual environments has alleviated many of thedifficulties and challenges associated with traditional general-purposecomputing. Machine and operating-system dependencies can besignificantly reduced or eliminated by packaging applications andoperating systems together as VMs and virtual appliances that executewithin virtual environments provided by virtualization layers running onmany different types of computer hardware. A next level of abstraction,referred to as virtual data centers or virtual infrastructure, provide adata-center interface to virtual data centers computationallyconstructed within physical data centers.

FIG. 7 shows virtual data centers provided as an abstraction ofunderlying physical-data-center hardware components. In FIG. 7, aphysical data center 702 is shown below a virtual-interface plane 704.The physical data center consists of a virtual-data-center managementserver computer 706 and any of different computers, such as PC 708, onwhich a virtual-data-center management interface may be displayed tosystem administrators and other users. The physical data centeradditionally includes generally large numbers of server computers, suchas server computer 710, that are coupled together by local areanetworks, such as local area network 712 that directly interconnectsserver computer 710 and 714-720 and a mass-storage array 722. Thephysical data center shown in FIG. 7 includes three local area networks712, 724, and 726 that each directly interconnects a bank of eightserver computers and a mass-storage array. The individual servercomputers, such as server computer 710, each includes a virtualizationlayer and runs multiple VMs. Different physical data centers may includemany different types of computers, networks, data-storage systems anddevices connected according to many different types of connectiontopologies. The virtual-interface plane 704, a logical abstraction layershown by a plane in FIG. 7, abstracts the physical data center to avirtual data center comprising one or more device pools, such as devicepools 730-732, one or more virtual data stores, such as virtual datastores 734-736, and one or more virtual networks. In certainimplementations, the device pools abstract banks of server computersdirectly interconnected by a local area network.

The virtual-data-center management interface allows provisioning andlaunching of VMs with respect to device pools, virtual data stores, andvirtual networks, so that virtual-data-center administrators need not beconcerned with the identities of physical-data-center components used toexecute particular VMs. Furthermore, the virtual-data-center managementserver computer 706 includes functionality to migrate running VMs fromone server computer to another in order to optimally or near optimallymanage device allocation, provides fault tolerance, and highavailability by migrating VMs to most effectively utilize underlyingphysical hardware devices, to replace VMs disabled by physical hardwareproblems and failures, and to ensure that multiple VMs supporting ahigh-availability virtual appliance are executing on multiple physicalcomputer systems so that the services provided by the virtual applianceare continuously accessible, even when one of the multiple virtualappliances becomes compute bound, data-access bound, suspends execution,or fails. Thus, the virtual data center layer of abstraction provides avirtual-data-center abstraction of physical data centers to simplifyprovisioning, launching, and maintenance of VMs and virtual appliancesas well as to provide high-level, distributed functionalities thatinvolve pooling the devices of individual server computers and migratingVMs among server computers to achieve load balancing, fault tolerance,and high availability.

FIG. 8 shows virtual-machine components of a virtual-data-centermanagement server computer and physical server computers of a physicaldata center above which a virtual-data-center interface is provided bythe virtual-data-center management server computer. Thevirtual-data-center management server computer 802 and avirtual-data-center database 804 comprise the physical components of themanagement component of the virtual data center. The virtual-data-centermanagement server computer 802 includes a hardware layer 806 andvirtualization layer 808 and runs a virtual-data-centermanagement-server VM 810 above the virtualization layer. Although shownas a single server computer in FIG. 8, the virtual-data-centermanagement server computer (“VDC management server”) may include two ormore physical server computers that support multipleVDC-management-server virtual appliances. The virtual-data-centermanagement-server VM 810 includes a management-interface component 812,distributed services 814, core services 816, and a host-managementinterface 818. The host-management interface 818 is accessed from any ofvarious computers, such as the PC 708 shown in FIG. 7. Thehost-management interface 818 allows the virtual-data-centeradministrator to configure a virtual data center, provision VMs, collectstatistics and view log files for the virtual data center, and to carryout other, similar management tasks. The host-management interface 818interfaces to virtual-data-center agents 824, 825, and 826 that executeas VMs within each of the server computers of the physical data centerthat is abstracted to a virtual data center by the VDC management servercomputer.

The distributed services 814 include a distributed-device scheduler thatassigns VMs to execute within particular physical server computers andthat migrates VMs in order to most effectively make use of computationalbandwidths, data-storage capacities, and network capacities of thephysical data center. The distributed services 814 further include ahigh-availability service that replicates and migrates VMs in order toensure that VMs continue to execute despite problems and failuresexperienced by physical hardware components. The distributed services814 also include a live-virtual-machine migration service thattemporarily halts execution of a VM, encapsulates the VM in an OVFpackage, transmits the OVF package to a different physical servercomputer, and restarts the VM on the different physical server computerfrom a virtual-machine state recorded when execution of the VM washalted. The distributed services 814 also include a distributed backupservice that provides centralized virtual-machine backup and restore.

The core services 816 provided by the VDC management server VM 810include host configuration, virtual-machine configuration,virtual-machine provisioning, generation of virtual-data-center alertsand events, ongoing event logging and statistics collection, a taskscheduler, and a device-management module. Each physical servercomputers 820-822 also includes a host-agent VM 828-830 through whichthe virtualization layer can be accessed via a virtual-infrastructureapplication programming interface (“API”). This interface allows aremote administrator or user to manage an individual server computerthrough the infrastructure API. The virtual-data-center agents 824-826access virtualization-layer server information through the host agents.The virtual-data-center agents are primarily responsible for offloadingcertain of the virtual-data-center management-server functions specificto a particular physical server to that physical server computer. Thevirtual-data-center agents relay and enforce device allocations made bythe VDC management server VM 810, relay virtual-machine provisioning andconfiguration-change commands to host agents, monitor and collectperformance statistics, alerts, and events communicated to thevirtual-data-center agents by the local host agents through theinterface API, and to carry out other, similar virtual-data-managementtasks.

The virtual-data-center abstraction provides a convenient and efficientlevel of abstraction for exposing the computational devices of acloud-computing facility to cloud-computing-infrastructure users. Acloud-director management server exposes virtual devices of acloud-computing facility to cloud-computing-infrastructure users. Inaddition, the cloud director introduces a multi-tenancy layer ofabstraction, which partitions VDCs into tenant-associated VDCs that caneach be allocated to a particular individual tenant or tenantorganization, both referred to as a “tenant.” A given tenant can beprovided one or more tenant-associated VDCs by a cloud director managingthe multi-tenancy layer of abstraction within a cloud-computingfacility. The cloud services interface (308 in FIG. 3) exposes avirtual-data-center management interface that abstracts the physicaldata center.

FIG. 9 shows a cloud-director level of abstraction. In FIG. 9, threedifferent physical data centers 902-904 are shown below planesrepresenting the cloud-director layer of abstraction 906-908. Above theplanes representing the cloud-director level of abstraction,multi-tenant virtual data centers 910-912 are shown. The devices ofthese multi-tenant virtual data centers are securely partitioned inorder to provide secure virtual data centers to multiple tenants, orcloud-services-accessing organizations. For example, acloud-services-provider virtual data center 910 is partitioned into fourdifferent tenant-associated virtual-data centers within a multi-tenantvirtual data center for four different tenants 916-919. Eachmulti-tenant virtual data center is managed by a cloud directorcomprising one or more cloud-director server computers 920-922 andassociated cloud-director databases 924-926. Each cloud-director servercomputer or server computers runs a cloud-director virtual appliance 930that includes a cloud-director management interface 932, a set ofcloud-director services 934, and a virtual-data-center management-serverinterface 936. The cloud-director services include an interface andtools for provisioning multi-tenant virtual data center virtual datacenters on behalf of tenants, tools and interfaces for configuring andmanaging tenant organizations, tools and services for organization ofvirtual data centers and tenant-associated virtual data centers withinthe multi-tenant virtual data center, services associated with templateand media catalogs, and provisioning of virtualization networks from anetwork pool. Templates are VMs that each contains an OS and/or one ormore VMs containing applications. A template may include much of thedetailed contents of VMs and virtual appliances that are encoded withinOVF packages, so that the task of configuring a VM or virtual applianceis significantly simplified, requiring only deployment of one OVFpackage. These templates are stored in catalogs within a tenant'svirtual-data center. These catalogs are used for developing and stagingnew virtual appliances and published catalogs are used for sharingtemplates in virtual appliances across organizations. Catalogs mayinclude OS images and other information relevant to construction,distribution, and provisioning of virtual appliances.

Considering FIGS. 7 and 9, the VDC-server and cloud-director layers ofabstraction can be seen, as discussed above, to facilitate employment ofthe virtual-data-center concept within private and public clouds.However, this level of abstraction does not fully facilitate aggregationof single-tenant and multi-tenant virtual data centers intoheterogeneous or homogeneous aggregations of cloud-computing facilities.

FIG. 10 shows virtual-cloud-connector nodes (“VCC nodes”) and a VCCserver, components of a distributed system that provides multi-cloudaggregation and that includes a cloud-connector server andcloud-connector nodes that cooperate to provide services that aredistributed across multiple clouds. VMware vCloud™ VCC servers and nodesare one example of VCC server and nodes. In FIG. 10, seven differentcloud-computing facilities are shown 1002-1008. Cloud-computing facility1002 is a private multi-tenant cloud with a cloud director 1010 thatinterfaces to a VDC management server 1012 to provide a multi-tenantprivate cloud comprising multiple tenant-associated virtual datacenters. The remaining cloud-computing facilities 1003-1008 may beeither public or private cloud-computing facilities and may besingle-tenant virtual data centers, such as virtual data centers 1003and 1006, multi-tenant virtual data centers, such as multi-tenantvirtual data centers 1004 and 1007-1008, or any of various differentkinds of third-party cloud-services facilities, such as third-partycloud-services facility 1005. An additional component, the VCC server1014, acting as a controller is included in the private cloud-computingfacility 1002 and interfaces to a VCC node 1016 that runs as a virtualappliance within the cloud director 1010. A VCC server may also run as avirtual appliance within a VDC management server that manages asingle-tenant private cloud. The VCC server 1014 additionallyinterfaces, through the Internet, to VCC node virtual appliancesexecuting within remote VDC management servers, remote cloud directors,or within the third-party cloud services 1018-1023. The VCC serverprovides a VCC server interface that can be displayed on a local orremote terminal, PC, or other computer system 1026 to allow acloud-aggregation administrator or other user to accessVCC-server-provided aggregate-cloud distributed services. In general,the cloud-computing facilities that together form amultiple-cloud-computing aggregation through distributed servicesprovided by the VCC server and VCC nodes are geographically andoperationally distinct.

As mentioned above, while the virtual-machine-based virtualizationlayers, described in the previous subsection, have received widespreadadoption and use in a variety of different environments, from personalcomputers to enormous distributed computing systems, traditionalvirtualization technologies are associated with computational overheads.While these computational overheads have steadily decreased, over theyears, and often represent ten percent or less of the totalcomputational bandwidth consumed by an application running above a guestoperating system in a virtualized environment, traditionalvirtualization technologies nonetheless involve computational costs inreturn for the power and flexibility that they provide.

While a traditional virtualization layer can simulate the hardwareinterface expected by any of many different operating systems, OSLvirtualization essentially provides a secure partition of the executionenvironment provided by a particular operating system. As one example,OSL virtualization provides a file system to each container, but thefile system provided to the container is essentially a view of apartition of the general file system provided by the underlyingoperating system of the host. In essence, OSL virtualization usesoperating-system features, such as namespace isolation, to isolate eachcontainer from the other containers running on the same host. In otherwords, namespace isolation ensures that each application is executedwithin the execution environment provided by a container to be isolatedfrom applications executing within the execution environments providedby the other containers. A container cannot access files not includedthe container's namespace and cannot interact with applications runningin other containers. As a result, a container can be booted up muchfaster than a VM, because the container uses operating-system-kernelfeatures that are already available and functioning within the host.Furthermore, the containers share computational bandwidth, memory,network bandwidth, and other computational resources provided by theoperating system, without the overhead associated with computationalresources allocated to VMs and virtualization layers. Again, however,OSL virtualization does not provide many desirable features oftraditional virtualization. As mentioned above, OSL virtualization doesnot provide a way to run different types of operating systems fordifferent groups of containers within the same host andOSL-virtualization does not provide for live migration of containersbetween hosts, high-availability functionality, distributed resourcescheduling, and other computational functionality provided bytraditional virtualization technologies.

FIG. 11 shows an example server computer used to host three containers.As discussed above with reference to FIG. 4, an operating system layer404 runs above the hardware 402 of the host computer. The operatingsystem provides an interface, for higher-level computational entities,that includes a system-call interface 428 and the non-privilegedinstructions, memory addresses, and registers 426 provided by thehardware layer 402. However, unlike in FIG. 4, in which applications rundirectly above the operating system layer 404, OSL virtualizationinvolves an OSL virtualization layer 1102 that provides operating-systeminterfaces 1104-1106 to each of the containers 1108-1110. Thecontainers, in turn, provide an execution environment for an applicationthat runs within the execution environment provided by container 1108.The container can be thought of as a partition of the resourcesgenerally available to higher-level computational entities through theoperating system interface 430.

FIG. 12 shows an approach to implementing the containers on a VM. FIG.12 shows a host computer similar to the host computer shown in FIG. 5A,discussed above. The host computer includes a hardware layer 502 and avirtualization layer 504 that provides a virtual hardware interface 508to a guest operating system 1102. Unlike in FIG. 5A, the guest operatingsystem interfaces to an OSL-virtualization layer 1104 that providescontainer execution environments 1206-1208 to multiple applicationprograms.

Although only a single guest operating system and OSL virtualizationlayer are shown in FIG. 12, a single virtualized host system can runmultiple different guest operating systems within multiple VMs, each ofwhich supports one or more OSL-virtualization containers. A virtualized,distributed computing system that uses guest operating systems runningwithin VMs to support OSL-virtualization layers to provide containersfor running applications is referred to, in the following discussion, asa “hybrid virtualized distributed computing system.”

Running containers above a guest operating system within a VM providesadvantages of traditional virtualization in addition to the advantagesof OSL virtualization. Containers can be quickly booted in order toprovide additional execution environments and associated resources foradditional application instances. The resources available to the guestoperating system are efficiently partitioned among the containersprovided by the OSL-virtualization layer 1204 in FIG. 12, because thereis almost no additional computational overhead associated withcontainer-based partitioning of computational resources. However, manyof the powerful and flexible features of the traditional virtualizationtechnology can be applied to VMs in which containers run above guestoperating systems, including live migration from one host to another,various types of high-availability and distributed resource scheduling,and other such features. Containers provide share-based allocation ofcomputational resources to groups of applications with guaranteedisolation of applications in one container from applications in theremaining containers executing above a guest operating system. Moreover,resource allocation can be modified at run time between containers. Thetraditional virtualization layer provides for flexible and scaling overlarge numbers of hosts within large distributed computing systems and asimple approach to operating-system upgrades and patches. Thus, the useof OSL virtualization above traditional virtualization in a hybridvirtualized distributed computing system, as shown in FIG. 12, providesmany of the advantages of both a traditional virtualization layer andthe advantages of OSL virtualization.

Process and System for Forecasting Time Series Data and AnomalyDetection in a Distributed Computing System

Processes and systems for forecasting time series data and detection ofanomalous behaving resources of a distributed computing system aredescribed below. The processes and systems provide three advantages overtypical forecasting and anomaly detection methods by: (1) minimizingresource utilization from the tenant side; (2) providing optimal speedof forecast execution and anomaly detection over other techniques forforecasting and anomaly detection; and (3) providing accurate forecastsof resource usage and adjust resource usage to accommodate theforecasted changes in resource usage. The time series data may begenerated by many physical and virtual resources of the distributedcomputing system.

FIG. 13A show an example of a virtualization layer 1302 located above aphysical data center 1304. For the sake of illustration, thevirtualization layer 1302 is separated from the physical data center1304 by a virtual-interface plane 1306. The physical data center 1304 isan example of a distributed computing system that comprises a managementserver computer 1308 and any of various computers, such as PC 1310, onwhich a virtual-data-center (“VDC”) management interface may bedisplayed to system administrators and other users. The physical datacenter 1304 additionally includes many server computers, such as servercomputers 1312-1319, coupled together by local area networks, such aslocal area network 1320 which interconnects server computers 1312-1319and a mass-storage array 1322. The physical data center 1304 includesthree local area networks that each directly interconnects a bank ofeight server computers and a mass-storage array. Different physical datacenters may include many different types of computers, networks,data-storage systems and devices connected according to many differenttypes of connection topologies. The virtualization layer 1302 includesvirtual objects, such as VMs and containers, hosted by the servercomputers in the physical data center 1304. The virtualization layer1302 may also include a virtual network (not illustrated) of virtualswitches, routers, and network interface cards formed from the physicalswitches, routers, and network interface cards of the physical datacenter 1304. Certain server computers host VMs as described above withreference to FIGS. 5A-5B. For example, server computer 1314 hosts twoVMs 1324, server computer 1326 hosts four VMs 1328, and server computer1330 hosts a VM 1332. Other server computers may host containers asdescribed above with reference to FIGS. 11 and 12. For example, servercomputer 1318 hosts four containers 1334. The virtual-interface plane1306 abstracts the resources of the physical data center 1304 to one ormore VDCs comprising the virtual objects and one or more virtual datastores, such as virtual data stores 1338 and 1340. For example, one VDCmay comprise VMs 1328 and virtual data store 1338 and another VDC maycomprise VMs 1324 and virtual data store 1340 that are connected overseparate virtual networks.

In the following discussion, the term “resource” refers to a physicalresource of a distributed computing system, such as, but are not limitedto, a processor, a core, memory, a network connection, networkinterface, data-storage device, a mass-storage device, a switch, arouter, and other any other component of the physical data center 1304.Resources of a server computer and clusters of server computers may forma resource pool for creating virtual resources of a virtualinfrastructure used to run virtual objects. The term “resource” may alsorefer to a virtual resource, which may have been formed from physicalresources assigned to a virtual object. For example, a resource may be avirtual processor used by a virtual object formed from one or more coresof a multicore processor, virtual memory formed from a portion ofphysical memory, virtual storage formed from a sector or image of a harddisk drive, a virtual switch, and a virtual router. Each virtual objectuses only the physical resources assigned to the virtual object.

In FIGS. 13B-13C, a monitor tool 1342 monitors physical and virtualresources by collecting numerous streams of time-dependent metric data,called “time series data,” from physical and virtual resources. Themonitoring tool 1342 processes the time series data, as described below,to forecast resource usage, generate alerts, and may generaterecommendations, or execute remedial measures, to reconfigure thevirtual network or migrate VMs or containers from one server computer toanother in order to most effectively utilize underlying physicalresources. For example, remedial measures include, but are not limitedto, replacing VMs disabled by physical hardware problems and failures,cloning VMs to ensure that the services provided by the VMs arecontinuously accessible, even when one of the VMs becomes compute boundor data-access bound. As shown in FIGS. 13B-13C, directional arrowsrepresent time series data sent from physical and virtual resources tothe monitoring tool 1342. In FIG. 13B, PC 1310, server computers 1308and 1312-1315, and mass-storage array 1322 send time series data to themonitoring tool 1342. Clusters of server computers may also send timeseries data to the monitoring tool 1342. For example, a cluster ofserver computers 1312-1315 sends cluster time series data to themonitoring tool 1342. In FIG. 13C, the VMs, containers, and virtualstorage send time series data to the monitoring tool 1342.

A sequence of time series data associated with a resource comprisesmetric data values indexed in time order and recorded in spaced pointsin time called “time steps.” A metric data value in a sequence of timeseries data is denoted byy _(i) =y(t _(i))  (1)

where

-   -   subscript i is a time step index; and    -   t_(i) is a time step indicating when the metric data point is        recorded in a data-storage device.

FIG. 14 shows a plot of an example sequence of time series dataassociated with a resource of a distributed computing system. Horizontalaxis 1402 represents time. Vertical axis 1404 represents a range ofmetric value amplitudes. Curve 1406 represents a sequence of time seriesdata for a metric associated with a physical or virtual resource. Inpractice, a sequence of time series data comprises discrete metric datavalues in which each metric value is recorded in a data-storage device.FIG. 14A includes a magnified view 1408 of three consecutive metric datavalues represented by points. Each point represents an amplitude of themetric at a corresponding time step. For example, points 1410-1412represents consecutive metric data values (i.e., amplitudes) y_(i−i),y_(i), and y_(i+1) recorded in a data-storage device at correspondingtime steps t_(i−1), t_(i), and t_(i+1). The example sequence of timeseries data may represent usage of a physical or virtual resource. Forexample, the time series data may represent CPU usage of a core in amulticore processor of a server computer over time. The time series datamay represent the amount of virtual memory a VM uses over time. The timeseries data may represent network throughput for a cluster of servercomputers. Network throughput is the number of bits of data transmittedto and from a physical or virtual object and is recorded in megabits,kilobits, or bits per second. The time series data may represent networktraffic for a cluster of server computers. Network traffic at a physicalor virtual object is a count of the number of data packets received andsent per unit of time.

FIG. 15 shows a high-level view of a process for forecasting time seriesdata and generating confidence bounds. The process comprises an off-linemode 1502 and an on-line mode 1504. Minimization of resource utilizationfrom the tenant side is accomplished by separating the training andforecasting procedures into off-line and on-line modes, respectively.Sequences of times series data generated for numerous physical andvirtual resources of the distributed computing system are recorded in atime series database 1506. For example, the time series database 1506includes physical and virtual CPU, memory, data packet delivery metrics,network throughput, network traffic, and application response times fornumerous resources running in the distributed computing system.Sequences of time series data generated for physical and virtualresources of a tenant environment of the distributed computing systemare also recorded in a separate time series database 1508. A tenantenvironment comprises server computers, virtual machines, containers,and network devices used to run the tenant's applications. For example,a tenant environment may be comprised of the physical and virtualresources of the tenant's VDC. In off-line mode 1502, historical timeseries data of the time series database 1506 are used to train arecurrent neural network (“RNN”) 1510 and compute confidence bounds ofthe time series database 1512. RNNs are a class of neural networks withconnections between nodes in the form a directed graph along a sequence.RNNs are designed to exhibits temporal dynamic behavior for time-basedsequences. Unlike traditional feedforward neural networks, RNNs useinternal state memory to process sequences of inputs. In addition, for atraditional neural network, it is assumed that all inputs and outputsare independent of each other. By contrast, RNNs are recurrent becauseRNNs perform the same computational task for every element of asequence, with the output dependent on the previous computations. Incertain implementations, a portion of the time series database 1506 usedto train the RNN may include the same data types that are found in thetenant environment. In other implementations, the entire time seriesdatabase 1506 may be used to train the RNN. The RNN may be a longshort-term memory neural network (“LSTM network”). LSTM networks areflexible at learning the behaviors of different types of time seriesdata. Because LSTM networks may be executed in a streaming manner, LSTMnetworks use fewer data points for forecasting than typical neuralnetworks and forecasting techniques. In the on-line mode 1504, for asequence of time series data 1514 associated with a resource of thetenant environment, confidence bounds of the time series data may becomputed 1516 and the RNN trained in the off-line mode 1504 may be usedto compute forecast time series data with confidence bounds over aforecast time window for the time series data 1514. Alternatively, theconfidence bounds of the time series database and the RNN are used tocompute forecast time series data with confidence bounds over theforecast time window. The tenant time series data 1514 may be timeseries data of a physical or virtual CPU, memory, data packet deliverymetrics, and application response time associated with running thetenant's application.

The process illustrated in FIG. 15 provides technological advantagesover other techniques for forecasting time series metric data: First,the trained RNN may be applied to time series data regardless ofsampling rate. Second, the trained RNN may be applied to any time seriesdata associated with any resource of the distributed computing system.Third, the trained RNN may be used to forecast time series data over atime horizon.

FIG. 16 shows a workflow of the off-line mode 1502 of FIG. 15. In block1602, the RNN is trained for the time series data of the time seriesdatabase 1506 as described below with reference to FIG. 17A. In block1604, the RNN may be stored in a data-storage device using JavaScriptobject notation (“json”) and h5 files 1606. A json file provides arecord of the RNN architecture, including the number of layers, thenumber of nodes in each layer, the type of activation functions utilizedfor each layer, and type of optimizers. An h5 file records weights ofthe RNN. In block 1608, the confidence bounds 1610 are computed for thetime series database 1506 as described below with reference to Equations(3)-(9) and FIG. 17B.

FIG. 17A shows training of the RNN in block 1602 of FIG. 6. The timeseries database comprises sequence of the time series data denoted byTSD₁, TSD₂, . . . , TSD_(Q), where Q is the number of selected sequencesof time series data in the time series database 1506 used to train theRNN. Each sequence of time series data is separately scaled by applyingthe following scaling to each metric value in the time series data:

$\begin{matrix}{{\overset{\_}{y}}_{i} = \frac{\left( {y_{i} - y_{m\; i\; n}} \right)}{\left( {y_{{ma}\; x} - y_{m\; i\; n}} \right)}} & (2)\end{matrix}$

where

-   -   y _(i) is a scaled time series data value that lies in the        interval [0,1];    -   y_(min) is the minimum metric value in the time series data; and    -   y_(max) is the maximum metric value in the time series data.        As shown in FIG. 17A, scaling is applied to each sequence of        time series data to obtain corresponding sequences of scaled        time series data followed by using the scaled time series data        to separately train the RNN. For example, scaling is applied to        the time series data TSD₁, in block 1702, to obtain        corresponding scaled time series data, which is then used to        train the RNN in block 1704. The RNN is trained again by        applying scaling to the time series data TSD₂, in block 1706, to        obtain corresponding scaled time series data, which is then used        to train the RNN in block 1708. Scaling followed by training the        same RNN with the scaled sequences of time series data is        carried for each of the Q selected sequences of time series        data. Because time series data is continuously being added to        sequences of the time series database 1506, after training the        RNN for each sequence of time series data, the training process        is repeated as represented by directional arrow 1710 current or        updated sequences of time series data until a saturation or        overfitting is obtained. The latest RNN is stored in json and h5        files and may be retrieved by the on-line mode 1504 at any time        while continuing to train the RNN model with the same or updated        time series database 1506.

The confidence bounds computed in block 1608 of FIG. 16 may be computedfor the full time series database 1506 or for selected sequences of timeseries data of the time series database 1506 that correspond to the timeseries data of the customer environment 1508 of FIG. 15. Consider Ksequences of time series data of the time series database 1506. The k-thsequence of time series data in the time series database 1506 is givenby:D _(k)=(y _(k,1) , . . . ,y _(k,N))  (3)where N is the number of metric values in the sequence of time seriesdata recorded at N time steps in the time interval [t₁, t_(N)]. Assumethe RNN trained in block 1602 of FIG. 16 receives I consecutive metricvalues of the k-th sequence as input and outputs O consecutive forecastmetric values as represented by(y _(k,1) , . . . ,y _(k,l))→RNN→(ŷ _(k,I+1) , . . . ,ŷ _(k,I+O))  (4)

where

-   -   (y_(k,1), . . . , y_(k,I)) is a sequence of historical time        series data of the time series database 1506;    -   (ŷ_(k,I+1), . . . , ŷ_(k,I+O)) is a sequence of forecast time        series data; and    -   N>I+O.        The time interval [t₁, t_(I)] of the sequence of time series        data (y₁, . . . , y_(I)) input to the RNN is called a        “historical time interval.” The time interval [t_(I+1), t_(I+O)]        for the forecast time series data (ŷ_(I+1), . . . , ŷ_(I+O))        output from the RNN is called a “current time interval.” Let        D_(k,historical)=(y_(k,1), . . . , y_(k,I)), {circumflex over        (D)}_(k,current)=(ŷ_(k,I+1), . . . , ŷ_(k,I+O)), and        D_(k,current)=(y_(k,I+1), . . . , y_(k,I+O)) be the sequence of        current time series data generated in the current time interval,        where D_(k)=D_(k,historical)∪D_(k,current). Let M=N−I−O+1 be the        number of historical sequences of the sequence of time series        data that are separately input to the RNN. For m=1, . . . , M,        forecast time series are computed as follows:        (y _(k,m) , . . . ,y _(k,I+m−1))→RNN→(ŷ _(k,I+m) , . . . ,ŷ        _(k,I+O+m−1))  (5a)        The historical time series data, current time series data, and        current forecast time series data are correspondingly        represented by        D _(k,historical) ^((m))=(y _(k,m) , . . . ,y _(k,I+m−1))  (5b)        D _(k,historical) ^((m))=(y _(k,I+m) , . . . ,y        _(k,I+O+m−1))  (5c)        {circumflex over (D)} _(k,current) ^((m))=(ŷ _(k,I+m) , . . . ,ŷ        _(k,I+O+m−1))  (5d)        For m=1, . . . , M, errors are computed between the current time        series data D_(k,current) ^((m)) and the current forecast time        series data D_(k,current) ^((m)) as follows:        e _(k) ^((m)) =D _(k,current) ^((m)) −{circumflex over (D)}        _(k,current) ^((m))=(y _(k,I+m) −ŷ _(k,I+m) , . . . ,y        _(k,I+O+m−1) −ŷ _(k,I+O+m−1))  (6)        Each error characterizes the accuracy of each component of the        sequence of current forecast time series data {circumflex over        (D)}_(k,current) ^((m)). The errors of the current forecast time        series data generated for the k-th sequence of time series data        in the time series database 1506 may be re-formulated to obtain        a set of forecast errors:        e _(k)=(e _(k,1) , . . . ,e _(k,O))  (7)        where each element of Equation (7) is a forecast error given by        e _(k,i) ={y _(k,I+i) −ŷ _(k,I+i)}.        In one implementation, the forecast error {y_(k,I+i)−ŷ_(k,I+i)}        may be the smallest error common

to  {e_(k)^((m))}_(m = 1)^(M).In an alternative implement, the forecast errors {y_(k,I+i)−ŷ_(k,I+i)}may be the first components of e_(k) ^((m)), because the first componentof a sequence of current forecast time series {circumflex over(D)}_(k,current) ^((m)) data is typically the closest to thecorresponding metric value of the current time series data D_(k,current)^((m)).

FIG. 17B shows computation of forecast errors for a sequence 1712 oftime series data of the time series database 1506. For the sake ofconvenience, the subscript k is omitted. The sequence of time seriesdata 1712 comprises N metric values. Overlapping subsequences 1714-1716of the sequence 1712 are sequences of historical time series data thatare separately input to the RNN, which outputs corresponding overlappingsequences of current forecast time series data 1718-1720. Forecastmetric values that are common to overlapping sequences of currentforecast time series data are different, because each sequence ofhistorical time series data is different. For example, forecast metricvalues 1722-1724 are generated for the first three sequences of currentforecast time series data 1718-1720. The forecast metric values1722-1724 are independently generated approximations of the actualmetric value y_(I+3). FIG. 17B shows sets of errors e⁽¹⁾, e⁽²⁾, e⁽³⁾, .. . , e^((M)) between the sequences of current forecast time series dataand the corresponding actual metric values of the sequences of currenttime series data 1712. FIG. 17B also shows a set of forecast errors eselected from the sets of errors e⁽¹⁾, e⁽²⁾, e⁽³⁾, . . . , e^((M)). Theforecast errors in the set of forecast errors e may be the smallest ofthe errors common to the sets of errors e⁽¹⁾, e⁽²⁾, e⁽³⁾, . . . ,e^((M)). For example, dashed line box 1726 identifies errors betweenthree different forecast metric values and the actual metric valuey_(I+3). The smallest of the three errors may be selected as theforecast error in the set of forecast errors e. In an alternativeimplementation, because the first component of the sequence of currentforecast time series data is typically the closest to the correspondingactual metric value of the current time series data, the errorassociated with the first component of each sequence of current forecasttime series data is selected as the forecast error in the set offorecast errors e. For example, dashed line 1728 corresponds to theerror associated with the first component 1724 of the sequence ofcurrent forecast time series data 1720.

Assuming the forecast errors e_(k,i) are normally distributed for k=1, .. . , K, the set of mean values for the forecast errors across the Ksequences of time series data in the time series database is given byμ=(μ₁,μ₂, . . . ,μ_(O))  (8a)and standard deviations for the forecast errors across the K sequencesof time series data in the time series database is given byσ=(σ₁,σ₂, . . . ,σ_(O))  (8b)

where the mean of the errors at the forecast time step t_(i) is given by

$\begin{matrix}{\mu_{i} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}\left( {y_{k,{I + i}} - {\hat{y}}_{k,{I + i}}} \right)}}} & \left( {8c} \right)\end{matrix}$and the standard deviation of the errors at the forecast time step t_(i)is given by

$\begin{matrix}{\sigma_{i} = \sqrt{\frac{\sum\limits_{k = 1}^{K}\left( {\left( {y_{k,{I + i}} - {\hat{y}}_{k,{I + i}}} \right) - \mu_{i}} \right)^{2}}{K - 1}}} & \left( {8d} \right)\end{matrix}$The upper confidence bounds for the time series database 1506 over thecurrent time window are given byupper=(upper₁, . . . ,upper_(O))  (9a)

where

-   -   upper_(i)=μ_(i)+z×σ_(i),        and the lower confidence bounds for the time series database        1506 over the current time window are given by        lower=(lower₁, . . . ,lower_(O))  (9b)

where

-   -   lower_(i)=μ_(i)−z×σ_(i)        In Equations (9a) and (9b), z is a user-selected number of        standard deviations from the mean, such as 1, 1.5, 2, 2.5, or 3.

FIG. 18 shows a workflow of the on-line mode 1504 of FIG. 15. Theon-line mode 1504 reads the information stored in the json and h5 filesand reconstructs the latest RNN generated by the off-line mode 1502. Theon-line mode 1504 may applies the confidence bounds computed in theoff-line mode 1502. The on-line mode 1504 applies the RNN to the timeseries data 1514 from a tenant environment to generate forecasted timeseries data over the forecast time window. The on-line mode 1504 maycompute forecast time series data with confidence bounds 1802 byapplying the confidence bounds of the time series database 1610 to theforecast time series data.

FIG. 19 shows a process for computing forecast time series data withconfidence bounds in the on-line mode 1504 for the time series data 1514from a tenant environment. In block 1902, scaling of Equation (2) isapplied to the time series data 1514 to obtain scaled time series data.In block 1904, parameters and weights of the RNN are read from the j sonand h5 files 1606 and the RNN is applied to the scaled time series datato obtain scaled forecast time series data 1906. In block 1908, inversescaling is applied to the scaled forecast time series data to obtainforecast time series data 1910. Inverse scaling may by carried bycomputingŷ _(i) =y _(i)(y _(max) −y _(min))+y _(min)  (10)

where ŷ_(i) is a forecast metric data value.

In block 1912, on-line mode 1504 may be used to compute confidencebounds for the time series data 1914. Let recorded time series datacollected for the resource in the forecast time window be denoted byy=(y ₁ , . . . ,y _(O))  (11a)Let forecast time series data computed in the forecast time window usingthe latest RNN be denoted byŷ=(ŷ ₁ , . . . ,ŷ _(O))  (11b)The forecast time window is the first current time window describedabove with reference to Equation (4). The forecast time series data inEquation (11b) are computed according to blocks 1902, 1904, and 1908 ofFIG. 19. The upper and lower confidence bounds for the time seriesdatabase in Equations (9a) and (9b) may be used to compute upper andlower confidence bounds over the forecast time window for the timeseries data y in Equation (11a) as follows:U _(i) =ŷ _(i)+upper_(i)×(y _(max) −y _(min))  (12a)L _(i) =ŷ _(i)−lower_(i)×(y _(max) −y _(min))  (12b)

where i=1, . . . , O.

The upper and lower confidence bounds are vectors with O number ofcomponents. In block 1916, the confidence bands are applied to theforecast time series data to obtain forecast time series data withconfidence bounds 1918.

Outliers are metric values of the time series data collected in theforecast time window that are located outside the upper and lowerconfidence bounds given by Equations (12a) and (12b). When a metricvalue y_(i) in the forecast time window satisfies the conditiony _(i) >U _(i)  (13a)where i=1, . . . , O, the metric value y_(i) is identified as anoutlier. When a metric value y_(i) in the forecast time window satisfiesthe conditiony _(i) <L _(i)  (13a)where i=1, . . . , O, the metric value y_(i) is identified as anoutlier. In an alternative implementation, the scaled time series datagiven by Equation (2) may be used to identify outlier metric values.When a scaled metric value y _(i) in the forecast time window satisfiesthe conditiony _(i)>upper_(i)  (14a)where i=1, . . . , O, the metric value y_(i) is identified as anoutlier. When a scaled metric value y _(i) in the forecast time windowsatisfies the conditiony _(i)<lower_(i)  (14a)where i=1, . . . , O, the metric value y_(i) is identified as anoutlier.

FIGS. 20A-20B illustrate computing forecast time series data in aforecast time window and applying confidence bounds to the forecast timeseries data. FIG. 20A shows a plot 2002 of time series data associatedwith a resource of a tenant environment. Horizontal axis 2004 representstime. Vertical axis 2006 represents a range of metric values for thetime series data. Curve 2008 represents time series data for the tenantenvironment. In block 2010, forecast time series data values arecomputed as described above with reference to blocks 1902, 1904, and1908 of FIG. 19. FIG. 20A show a plot 2012 of time series data 2008 withforecast time series data represented by dashed curve 2014 computed overa forecast time window 2016. The forecast time series data in theforecast time window may be used to adjust future resource usage. Forexample, the forecast time series data may indicate that resource usageby a tenant's application is expected to increase over the forecast timeinterval. Preemptive measures may include increasing the amount of theresource available to the application using the resource. On the otherhand, the forecast time series data may indicate that resource usage isexpected to decrease over the forecast time interval. In this case, theamount of the resource available to the tenant's application isdecreased and made available to other applications in order to avoidwastage of the resource. FIG. 20B shows a plot 2018 of time series dataaccumulated in the forecast time series data as represented curve 2020.Points 2022 and 2024 are potential outlier metric values. In block 2026,when time series data has accumulated in the forecast time window 2016,confidence bounds 2028 may be applied to the forecast time series datain the forecast time window 2016. The confidence bounds 2026 may be theconfidence bounds for the time series database given by Equations (12a)and (12b). FIG. 20B shows a plot 2030 with forecast time series data andconfidence bounds added to the time series data in the forecast timewindow 2016. Curve 2032 represent upper confidence bounds over theforecast time window 2012. Curve 2034 represent lower confidence boundsover the forecast time window 2012. Metric data values 2022 and 2024 arelocated outside the upper and lower confidence bounds and are identifiedas outliers, which may trigger an alert indicating anomalous behavior atthe resource.

Anomalous behavior of a resource of a tenant environment may bedetermined by the number of times the upper confidence bound forresource is violated or the number of times the lower confidence boundfor the resource is violated per unit of time. Let T denote the durationof a time horizon. The time interval may comprise the L more recentforecast time windows, where L is a positive integer. Letup−outlier−rate_(R) be a count of the number of upper confidence-boundviolations of the condition in Equation (14a) within the time horizon T,where the subscript R denotes a resource. When the following conditionis satisfiedup−outlier−rate_(R) >Th _(up)  (15a)where Th_(up) is a threshold for the number of upper confidence-boundviolations per unit of time, an alert may be displayed on the VDCmanagement interface with the corresponding resource identified asbehaving anomalously. Let low−outlier−rate_(R) be a count of the numberof lower confidence-bound violations of the condition in Equation (14b)within the time interval T. When the following condition is satisfiedlow−outlier−rate_(R) >Th _(low)  (15b)where Th_(low) is a threshold for the number of lower confidence-boundviolations per unit of time, an alert may also be displayed on the VDCmanagement interface with the corresponding resource identified asbehaving anomalously.

In an alternative implementation, the rates may be summed for theresources used by VMs, containers, server computers, cluster of VMs, orclusters of server computers to identify anomalous behaving VMs,containers, server computers, cluster of VMs, or clusters of servercomputers. When the following condition is satisfied

$\begin{matrix}{{{\sum\limits_{R}{up}} - {outlier} - {rate}_{R}} > {Thresh}_{up}} & \left( {16a} \right)\end{matrix}$where Thresh_(up) is a threshold for the number of upperconfidence-bound violations per unit of time, an alert may be displayedon the VDC management interface with the corresponding resources, VM,container, or server computers identified as behaving anomalously. Whenthe following condition is satisfied

$\begin{matrix}{{{\sum\limits_{R}{low}} - {outlier} - {rate}_{R}} > {Thresh}_{low}} & \left( {16b} \right)\end{matrix}$where Thresh_(low) is a threshold for the number of lowerconfidence-bound violations per unit of time, an alert may also bedisplayed on the VDC management interface with the correspondingresources, VM, container, or server computers identified as behavinganomalously.

When either of the conditions in Equations (15a) or (15b), or Equations(16a) and (16b), is satisfied, appropriate remedial measures may beexecuted to correct problems created by the anomalous behaving resource.The remedial measures may be executed to ensure the anomalous behavingresources do not hinder performance of the distributed computing system.For example, remedial measures include, but are not limited to, (1)decreasing the amount of the reserved capacity of the resource, whichincreases the usable capacity of the resource, (2) assigning one or moreadditional resources of the same type to the virtual object using theanomalous behaving resource, (3) migrating a virtual object that uses ananomalous behaving resource to a different server computer with the sametype of resource, (4) reclaiming under used resources for use by othervirtual objects, and (5) cloning one or more additional virtual objectsfrom a template of the virtual object using the anomalous behavingresource, the additional virtual objects to share the workload of thevirtual object.

FIGS. 21A-21J show plots of results obtained from training and using anRNN to forecast time series data and generate confidence bounds for CPUand memory time series data. FIG. 21A shows an example plot of 79 CPUmetrics in a time series database linked together with a 1-minute samplerate in which 80% were used to train LSTM RNN and 20% were used forvalidation. Twenty data points where used with a 1-hour minoringinterval to predict the next 10 points with 1-hour monitoring interval.FIG. 21B show corresponding residuals with 10 different residual graphscorresponding to each forecasted data point. As expected, the closestpoints have smaller errors:

averages of residuals

-   -   [0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 0.8, 0.9, 1.03, 1.15]

standard deviations of residuals

-   -   [2.7, 3.4, 3.7, 3.99, 4.2, 4.4, 4.6, 4.8, 4.97, 5.1].        Average of residuals and standard deviations of residuals have        increasing components. FIGS. 21C and 21D show averaged values of        residuals. More specifically, if the residuals are given        r=y−ŷ=(y ₁ −ŷ ₁ , . . . ,y _(O) −ŷ _(O))        then the mean absolute error of the residuals is given by

$r_{MAE} = {\frac{1}{O}{\sum\limits_{k = 1}^{O}{r_{k}}}}$where |⋅| denotes absolute value. With exception for the spikes, FIG.21C shows that most residual values are within 0-10%. FIGS. 21E-21J showtime series data (“Raw Data”), the forecasted time series data(“Forecast”), and the corresponding confidence bounds computed inforecast time window. For example, in FIG. 21E, dashed line 2102represents time series data associated with memory, thick dashed line2104 represents forecast time series data, and shaded, horn-shapesurfaces, such as shade, horn-shaped surface 2106, represent confidencebounds computed for separate forecast time windows. FIGS. 21-21J alsoshow examples of time series data values that appear outside of upperand lower confidence bounds. For example, metric value 2108, in FIG.21E, is an outlier and a candidate for anomaly inspection. When a timeseries metric data value is located outside the confidence bounds, andalert may be generated, indicating that the tenant's resources orapplications are exhibiting anomalous behavior. For example, in FIG.21J, time series data values violate upper and lower confidence boundscomputed during forecasting. The violations of the confidence boundsshown in FIG. 21J may trigger alerts indicating a problem with thememory used to run the tenant's applications.

The methods described below with reference to FIGS. 22-28 are stored inone or more data-storage devices as machine-readable instructions thatwhen executed by one or more processors of the computer system shown inFIG. 1 to compute forecast time series data and identify anomalousbehaving resources of a distributed computing system.

FIG. 22 shows a control-flow diagram of a method to compute forecasttime series data and identify anomalous behaving resources of adistributed computing system. In block 2201, the routine “train RNNbased on historical time series database and compute confidence boundsof time series database” is called. A loop beginning with block 2202repeatedly executes the computational operations represented by blocks2203-2210 for each resource of a tenant's environment. In block 2203,logical variables “Upper_outlier” and “Lower_outlier” are set to FALSE.A loop beginning with block 2204 repeatedly execute the computationaloperations represented by blocks 2205-2209 for each forecast timewindow. In block 2205, the routine “compute forecast time series data inforecast time window” is called. In block 2206, the routine “identifyanomalous behavior of resource based on confidence bounds” is called. Indecision block 2207, when abnormal behavior of a resource has beenidentified in block 2206, control flow to block 2208. In block 2208, theroutine “report anomalous behavior/execute remedial measures” is called.In decision block 2209, when forecasting is to be carried out foranother forecast time window, control returns to block 2203. In decisionblock 2210, when another resource is to be checked for anomalousbehavior, control returns to block 2205

FIG. 23 shows a control-flow diagram of routine “train RNN based onhistorical time series database and compute confidence bounds of timeseries database” called in block 2201 of FIG. 22. In block 2301, timeseries data of the time series database is read. In block 2302, theroutine “train RNN using time series database” is called. In block 2303,the routine “compute confidence bounds for the time series database” iscalled. In block 2305, parameters and weights for the RNN and theconfidence bounds are stored.

FIG. 24 shows a control-flow diagram of the routine “train RNN usingtime series database” called in block 2302 of FIG. 23. In decision block2401, while times series data continues to be recorded in the timeseries database, the computational operations represented by blocks2402-2406 are repeated. A loop beginning with block 2402 repeats thecomputational operations represented by blocks 2403-2406. In block 2403,the time series data is scaled as described above with reference toEquation (2). In block 2404, the RNN is trained based on the scaled timeseries data. In block 2405, the RNN is stored as a json and h5 files. Indecision block 2404, blocks 2403-2406 are repeated for another sequenceof time series data.

FIG. 25 shows a control-flow diagram of the routine “compute confidencebounds for the time series database” called in block 2303 of FIG. 23. Aloop beginning with block 2501 repeats the computational operationsrepresented by blocks 2502-2507 for K selected sequences of time seriesdata of the time series database 1506. A loop beginning with block 2502repeats the computational operations represented by blocks 2503-2505 foreach sequence of historical time series data. In block 2503, a sequenceof current forecast time series data is computed using the RNN, asdescribed above with reference to Equation (4). In block 2504, errorsare computed between the sequence of current forecast time series dataand the corresponding sequence of current time series data, as describedabove with reference to Equation (6). In decision block 2505, whenerrors have been computed for each sequence of historical time seriesdata, control flows to block 2506. In block 2506, the errors of thesequences of current forecast time series data are re-formulated toobtain a set of forecast errors for the k-th sequence, as describedabove with reference to Equation (7) and FIG. 17B. In decision block2507, when index k equals K, control flows to block 2508. In block 2508,mean errors are computed for the time series database 1506 as describedabove with reference to Equation (8a). In block 2509, standarddeviations are computed for the time series database 1506 as describedabove with reference to Equation (8b). In block 2510, upper confidencebounds are computed for the time series database as described above withreference to Equation (9a). In block 2511, lower confidence bounds arecomputed for the time series database as described above with referenceto Equation (9b).

FIG. 26 shows a control-flow diagram of the routine “compute forecasttime series data in forecast time window” called in block 2205 of FIG.26. In block 2601, time series data associated with a resource oftenant's environment is read from a time series database from thetenant's environment. In block 2602, scaling is applied to the timeseries data as described above with reference to Equation (2) to obtainscaled time series data associated with the resource. In block 2603, theRNN computed in block 2602 is applied to scaled time series data tocompute scaled forecast time series data over a forecast time window. Inblock 2604, inverse scaling is applied to the scaled forecast timeseries data as described above with reference to Equation (10).

FIG. 27 shows a control-flow diagram of the routine “identify abnormalbehavior of resource based on confidence bounds” called in block 2206 ofFIG. 22. A loop beginning with block 2701 repeats the computationaloperations represented by blocks 2702-2710 for each metric valueassociated with the resource in the forecast time window. In decisionblock 2701, when the metric value satisfies the condition given byEquation (12a), control flows to block 2703. In block 2703, the numberof upper confidence-bound violations within the time horizon,up−outlier−rate, is updated. In decision block 2704, when the conditiongiven by Equation (13a) is satisfied, control flows to block 2705. Inblock 2705, the resource is regarded as exhibiting anomalous behaviorand the logic variable Upper_outlier is assigned the logical value TRUE.In decision block 2706, when the metric value satisfies the conditiongiven by Equation (12b), control flows to block 2707. In block 2707, thenumber of lower confidence-bound violations within the time horizon,low−outlier−rate, is updated. In decision block 2708, when the conditiongiven by Equation (13b) is satisfied, control flows to block 2709. Inblock 2709, the resource is regarded as exhibiting anomalous behaviorand the logic variable Lower_outlier is assigned the logical value TRUE.In decision block 2710, control returns to decision block 2703 foranother metric value.

FIG. 28 shows a control-flow diagram of the routine “report abnormalbehavior/execute remedial measures” called in block 2208 of FIG. 22. Indecision block 2801, the logical variable Upper_outlier is TRUE, controlflows to block 2802. In block 2802, an alert is generated on themanagement consul indicating that upper confidence bounds for theresource have been violation and the resource is behaving in ananomalous manner. In block 2803, remedial measures are executed tocorrect the anomalous behavior associated with the resource. In decisionblock 2804, the logical variable Lower_outlier is TRUE, control flows toblock 2805. In block 2805, an alert is generated on the managementconsul indicating that lower confidence bounds for the resource havebeen violated and the resource is behaving in an anomalous manner. Inblock 2806, remedial measures are executed to correct the anomalousbehavior associated with the resource.

It is appreciated that the previous description of the disclosedembodiments is provided to enable any person skilled in the art to makeor use the present disclosure. Various modifications to theseembodiments will be apparent to those skilled in the art, and thegeneric principles defined herein may be applied to other embodimentswithout departing from the spirit or scope of the disclosure. Thus, thepresent disclosure is not intended to be limited to the embodimentsshown herein but is to be accorded the widest scope consistent with theprinciples and novel features disclosed herein.

The invention claimed is:
 1. In a process stored in one or moredata-storage devices and executed using one or more processors of acomputer system to forecast time series data and detect an anomalousbehaving resource of a distributed computing system, the improvementcomprising: continuously training a recurrent neural network (“RNN”)based on a time series database of continuously recorded time seriesdata for resources that run in the distributed computing system; for aresource used to run a tenant's applications in a tenant environment ofthe distributed computing system, using a latest trained RNN to generateforecast time series data in a forecast time window from recorded timeseries data associated with the resource; computing confidence boundsfor time series data generated in the forecast time interval using timeseries data of the time series database; and identifying anomalousbehavior of the resource based on at least one metric value of the timeseries data in the forecast time interval violating one of theconfidence bounds, thereby enabling execution of remedial measures thatovercome the anomalous behavior and improve execution of the tenant'sapplications in the tenant environment.
 2. The process of claim 1wherein continuously training the RNN based on the time series databasecomprises: while time series data associated with the resources of thedistributed computing systems are added to the time series database, foreach sequence of time series data of the time series database, scalingeach sequence of time series data; training the RNN using each sequenceof scaled time series data to obtain a latest trained RNN; and storingthe latest RNN in a data-storage device.
 3. The process of claim 1wherein using the latest trained RNN to generate the forecast timeseries data in the forecast time interval comprises: retrieving therecorded time series data associated with the resource from a timeseries database of the tenant environment; applying scaling to therecorded time series data to generate scaled time series data; applyingthe RNN to the scaled time series data to generate scaled forecast timeseries data; and applying inverse scaling to the scaled forecast timeseries data to generate the forecast time series data.
 4. The process ofclaim 1 wherein computing the confidence bounds for the time series datagenerated in the forecast time interval comprises: for each selectedsequence of time series data of the time series database, using the RNNto compute overlapping sequences of current forecast time series dataover current time intervals based on overlapping sequences of historicaltime series data of the selected sequence of time series data, andcomputing errors between the overlapping sequence of current forecasttime series data and corresponding overlapping sequence of current timeseries data; forming a set of forecast errors from the errors computedfor each of the selected sequences of time series data; computing meanerrors of the forecast errors across the sequences of time series datain the time series database based on the set of forecast errors;computing standard deviations of the forecast errors across thesequences of time series data in the time series database based on theset of forecast errors and the mean errors: computing upper confidencebounds for the forecast time series data based on the mean errors andthe standard deviations; and computing lower confidence bounds for theforecast time series data based on the mean errors and the standarddeviations.
 5. The process of claim 1 wherein identifying the anomalousbehavior of the resource comprises: for each metric value of the timeseries data generated in the forecast time interval, updating a count ofupper confidence-bound violations within a time horizon, when the metricvalue is greater than an upper confidence bound at a time step of themetric value, and updating a count of lower confidence-bound violationswithin a time horizon, when the metric value is less than a lowerconfidence bound at a time step of the metric value; identifyinganomalous behavior of the resource when the count of theupper-confidence bound violations is greater than a threshold for upperconfidence-bound violations per unit of time; and identifying anomalousbehavior of the resource when the count of the lower-confidence boundviolations is less than a threshold for lower confidence-boundviolations per unit of time.
 6. A computer system to forecast timeseries data and detect an anomalous behaving resource of a distributedcomputing system, the system comprising: one or more processors; one ormore data-storage devices; and machine-readable instructions stored inthe one or more data-storage devices that when executed using the one ormore processors controls the system to execute operations comprising:continuously training a recurrent neural network (“RNN”) based on a timeseries database of continuously recorded time series data for resourcesthat run in the distributed computing system; for a resource used to runa tenant's applications in a tenant environment of the distributedcomputing system, using a latest trained RNN to generate forecast timeseries data in a forecast time window from recorded time series dataassociated with the resource; computing confidence bounds for timeseries data generated in the forecast time interval using time seriesdata of the time series database; and identifying anomalous behavior ofthe resource based on at least one metric value of the time series datain the forecast time interval violating one of the confidence bounds. 7.The computer system of claim 6 wherein continuously training the RNNbased on the time series database comprises: while time series dataassociated with the resources of the distributed computing systems areadded to the time series database, for each sequence of time series dataof the time series database, scaling each sequence of time series data;training the RNN using each sequence of scaled time series data toobtain a latest trained RNN; and storing the latest RNN in adata-storage device.
 8. The computer system of claim 6 wherein using thelatest trained RNN to generate the forecast time series data in theforecast time interval comprises: retrieving the recorded time seriesdata associated with the resource from a time series database of thetenant environment; applying scaling to the recorded time series data togenerate scaled time series data; applying the RNN to the scaled timeseries data to generate scaled forecast time series data; and applyinginverse scaling to the scaled forecast time series data to generate theforecast time series data.
 9. The computer system of claim 6 whereincomputing the confidence bounds for the time series data generated inthe forecast time interval comprises: for each selected sequence of timeseries data of the time series database, using the RNN to computeoverlapping sequences of current forecast time series data over currenttime intervals based on overlapping sequences of historical time seriesdata of the selected sequence of time series data, and computing errorsbetween the overlapping sequence of current forecast time series dataand corresponding overlapping sequence of current time series data;forming a set of forecast errors from the errors computed for each ofthe selected sequences of time series data; computing mean errors of theforecast errors across the sequences of time series data in the timeseries database based on the set of forecast errors; computing standarddeviations of the forecast errors across the sequences of time seriesdata in the time series database based on the set of forecast errors andthe mean errors: computing upper confidence bounds for the forecast timeseries data based on the mean errors and the standard deviations; andcomputing lower confidence bounds for the forecast time series databased on the mean errors and the standard deviations.
 10. The computersystem of claim 6 wherein identifying the anomalous behavior of theresource comprises: for each metric value of the time series datagenerated in the forecast time interval, updating a count of upperconfidence-bound violations within a time horizon, when the metric valueis greater than an upper confidence bound at a time step of the metricvalue, and updating a count of lower confidence-bound violations withina time horizon, when the metric value is less than a lower confidencebound at a time step of the metric value; identifying anomalous behaviorof the resource when the count of the upper-confidence bound violationsis greater than a threshold for upper confidence-bound violations perunit of time; and identifying anomalous behavior of the resource whenthe count of the lower-confidence bound violations is less than athreshold for lower confidence-bound violations per unit of time.
 11. Anon-transitory computer-readable medium encoded with machine-readableinstructions that implement a method carried out by one or moreprocessors of a computer system to execute operations comprising:continuously training a recurrent neural network (“RNN”) based on a timeseries database of continuously recorded time series data for resourcesthat run in a distributed computing system; for a resource used to run atenant's applications in a tenant environment of the distributedcomputing system, using a latest trained RNN to generate forecast timeseries data in a forecast time window from recorded time series dataassociated with the resource: computing confidence bounds for timeseries data generated in the forecast time interval using time seriesdata of the time series database; and identifying anomalous behavior ofthe resource based on at least one metric value of the time series datain the forecast time interval violating one of the confidence bounds,thereby enabling execution of remedial measures that overcome theanomalous behavior and improve execution of the tenant's applications inthe tenant environment.
 12. The medium of claim 1 wherein continuouslytraining the RNN based on the time series database comprises: while timeseries data associated with the resources of the distributed computingsystems are added to the time series database, for each sequence of timeseries data of the time series database, scaling each sequence of timeseries data; training the RNN using each sequence of scaled time seriesdata to obtain a latest trained RNN; and storing the latest RNN in adata-storage device.
 13. The medium of claim 11 wherein using the latesttrained RNN to generate the forecast time series data in the forecasttime interval comprises: retrieving the recorded time series dataassociated with the resource from a time series database of the tenantenvironment; applying scaling to the recorded time series data togenerate scaled time series data; applying the RNN to the scaled timeseries data to generate scaled forecast time series data; and applyinginverse scaling to the scaled forecast time series data to generate theforecast time series data.
 14. The medium of claim 11 wherein computingthe confidence bounds for the time series data generated in the forecasttime interval comprises: for each selected sequence of time series dataof the time series database, using the RNN to compute overlappingsequences of current forecast time series data over current timeintervals based on overlapping sequences of historical time series dataof the selected sequence of time series data, and computing errorsbetween the overlapping sequence of current forecast time series dataand corresponding overlapping sequence of current time series data;forming a set of forecast errors from the errors computed for each ofthe selected sequences of time series data; computing mean errors of theforecast errors across the sequences of time series data in the timeseries database based on the set of forecast errors; computing standarddeviations of the forecast errors across the sequences of time seriesdata in the time series database based on the set of forecast errors andthe mean errors; computing upper confidence bounds for the forecast timeseries data based on the mean errors and the standard deviations; andcomputing lower confidence bounds for the forecast time series databased on the mean errors and the standard deviations.
 15. The medium ofclaim 11 wherein identifying the anomalous behavior of the resourcecomprises: for each metric value of the time series data generated inthe forecast time interval, updating a count of upper confidence-boundviolations within a time horizon, when the metric value is greater thanan upper confidence bound at a time step of the metric value, andupdating a count of lower confidence-bound violations within a timehorizon, when the metric value is less than a lower confidence bound ata time step of the metric value; identifying anomalous behavior of theresource when the count of the upper-confidence bound violations isgreater than a threshold for upper confidence-bound violations per unitof time; and identifying anomalous behavior of the resource when thecount of the lower-confidence bound violations is less than a thresholdfor lower confidence-bound violations per unit of time.